On the geometry of orbit closures for representation-infinite algebras

TL;DR

This paper explores the geometric properties of orbit closures in representation-infinite algebras, extending known examples from the Kronecker algebra to a broader class with preprojective components.

Contribution

It generalizes the example of non-unibranch, non-Cohen-Macaulay orbit closures from the Kronecker algebra to all representation-infinite algebras with preprojective components.

Findings

Orbit closures are neither unibranch nor Cohen-Macaulay in the extended class.

The example from the Kronecker algebra can be generalized to a wider class of algebras.

Provides insights into the geometric complexity of module varieties for infinite representation type.

Abstract

For the Kronecker algebra, Zwara found in [14] an example of a module whose orbit closure is neither unibranch nor Cohen-Macaulay. In this paper, we explain how to extend this example to all representation-infinite algebras with a preprojective component.